Question

A fire truck travels down the highway at the speed of 120 km/h. Its siren has an emitting sounds at a frequency of 4 x 10⁴ Hz. 

a) What is heard by the passenger in the car traveling at 100 km/h in opposite direction, when the sound velocity is 340 m/s?

b) What will happen in the frequency heard if the direction of the two vehicles will be approaching each other?

Answer 1

a) We can find the frequency from the Doppler Shift formula:

$$f_o=f_s(\dfrac{v-v_0}{v+v_s}),$$ $$f_o=4\cdot10^4\ Hz\cdot(\dfrac{340\ \dfrac{m}{s}-27.77\ \dfrac{m}{s}}{340\ \dfrac{m}{s}+33.33\ \dfrac{m}{s}})=3.34\cdot10^4\ Hz.$$

(b) We can find the frequency from the Doppler Shift formula:

$$f_o=f_s(\dfrac{v+v_0}{v-v_s}),$$ $$f_o=4\cdot10^4\ Hz\cdot(\dfrac{340\ \dfrac{m}{s}+27.77\ \dfrac{m}{s}}{340\ \dfrac{m}{s}-33.33\ \dfrac{m}{s}})=4.8\cdot10^4\ Hz.$$